Question

Решите уравнение (3x-5)^2-16=0

Answer 1

(3х-5)^2 - 16=0
(3х-5)^2-4^2 =0
(3х-5-4)*(3х-5+4)=0
(3х-9)*(3х-1)=0
3х-9=0, либо 3х-1=0
х=3. х=1/3
Ответ = х=3,х=1/3

Answer 2

(3х-5)^2-16=0

9x^2-30x+25-16=9

9x^2-30x+9=0

D=b^2-4a×c

b=(-30),a=9,c=9

D=(-30)^2-4×9×9=576 D>0

x1= 30-24/9×2= 6/18 =1/3

х2=30+24/9×2=54/18=3

x1,x2 вычисляются по формуле

Ответ:х1=1/3;х2=3

Answer 3

To solve the equation (3x - 5)^2 - 16 = 0, follow these steps:

Step 1: Expand the squared term. Step 2: Combine like terms. Step 3: Isolate the variable. Step 4: Solve for x.

Let's go through each step:

Step 1: Expand the squared term (3x - 5)^2 = (3x - 5) * (3x - 5) = 9x^2 - 15x - 15x + 25 = 9x^2 - 30x + 25

Step 2: Combine like terms Now the equation becomes: 9x^2 - 30x + 25 - 16 = 0

Step 3: Isolate the variable To isolate x, move the constant term to the right side: 9x^2 - 30x + 9 = 0

Step 4: Solve for x To solve this quadratic equation, you can use factoring or the quadratic formula. In this case, let's use factoring.

The equation can be factored as follows: (3x - 3)(3x - 3) = 0

Now, set each factor to zero and solve for x:

1. 3x - 3 = 0 3x = 3 x = 3/3 x = 1

2. 3x - 3 = 0 3x = 3 x = 3/3 x = 1

So, the solution to the equation is x = 1.